微分中值定理“中间点”的渐近性

为了研究区间两端点同时趋近于一定点时,柯西微分中值定理"中间点"的渐近性,利用二元函数洛必达法则建立了柯西微分中值定理"中间点"的渐近估计式。与已有文献使用的方法相比,该方法证明过程简练,所得结果新颖,并推广、改进了有关文献中的结果。

Asymptotic Behavior of "Intermediate Point" for Differential Mean Value Theorem

The purpose of this paper is to study the asymptotic behavior of the "intermediate point" of Cauchy differential mean value theorem when the two ends of the interval approach a certain point at the same time. By using the L''Hospital''s rule of binary function, the asymptotic estimates of the "intermediate point" of Cauchy differential mean value theorem are established.Compared with the previous studies, this paper uses the L''Hospital''s rule of binary function to study its asymptotic behavior, which makes the proof process concise. The results obtained in this paper are original,canimprove and extend the corresponding results of some references.